Related papers: Switching for Small Strongly Regular Graphs
The series-parallel (SP) graphs are those containing no topological $K_{_4}$ and are considered trivial. We relax the prohibition distinguishing the SP graphs by forbidding only embeddings of $K_{_4}$ whose edges with both ends 3-valent…
We study the structural constraint of random scale-free networks that determines possible combinations of the degree exponent $\gamma$ and the upper cutoff $k_c$ in the thermodynamic limit. We employ the framework of graphicality…
In this work, we give novel spectral norm bounds for graph matrix on inputs being random regular graphs. Graph matrix is a family of random matrices with entries given by polynomial functions of the underlying input. These matrices have…
We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.
For a graph G and an integer t we let mcc_t(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having more than m vertices. Let F be any nontrivial minor-closed…
We provide an upper bound to the number of graph homomorphisms from $G$ to $H$, where $H$ is a fixed graph with certain properties, and $G$ varies over all $N$-vertex, $d$-regular graphs. This result generalizes a recently resolved…
The operation of switching a graph $\Gamma$ with respect to a subset $X$ of the vertex set interchanges edges and non-edges between $X$ and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set…
Let $k,p,q$ be three positive integers. A graph $G$ with order $n$ is said to be $k$-placeable if there are $k$ edge disjoint copies of $G$ in the complete graph on $n$ vertices. A $(p,\,q)$-graph is a graph of order $p$ with $q$ edges.…
The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup…
In this paper, we study orthogonal colourings of random geometric graphs. Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive…
This paper examines the spectral characterizations of oriented graphs. Let $\Sigma$ be an $n$-vertex oriented graph with skew-adjacency matrix $S$. Previous research mainly focused on self-converse oriented graphs, proposing arithmetic…
In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
In this paper, we introduce a method for finding all edge-transitive graphs of small order, using faithful representations of transitive permutation groups of small degree, and we explain how we used this method to find all edge-transitive…
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected values. We call graphs with this property for all subgraphs with…
It was proved in [Y.-Q. Feng, C. H. Li and J.-X. Zhou, Symmetric cubic graphs with solvable automorphism groups, {\em European J. Combin.} {\bf 45} (2015), 1-11] that a cubic symmetric graph with a solvable automorphism group is either a…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Weak and strong coloring numbers are generalizations of the degeneracy of a graph, where for each natural number $k$, we seek a vertex ordering such every vertex can (weakly respectively strongly) reach in $k$ steps only few vertices with…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…